Electrical hybrid ring network



Feb. 21, 1956 A. E. HYLAS ETAL 2,735,986

ELECTRICAL HYBRID RING NETWORK o INVENTORS c WALTER V TYM/NSKI BY ALBERT E. HYLAS Fig. 2

6 A TTORNE Y5 Feb. 21, 1956 HYLAs r 2,735,986 I ELECTRICAL HYBRID RING NETWORK Filed March 5, 1953 4 Sheets-Sheet 3 E] o E 8 o m E g 3 w o Q E E :0 d5 4 N O 5 co 5:

z Q I 2 q: N5 0 g H) (DJ N 3 d5 3:

n: o N (E v n: w m w g 3 Q\ 0 a x :1 E m 0 5 C lw w n: O 3

0 0 O O :0 N

ifiO HBMOd .LNEIOHHd ind INVENTORS WALTER M TYM/NSKI BY ALBERT E. HYLAS ag) v I TTORNEYS Feb. 21, 1956 A. E. HYLAS ETAL 2,735,986

ELECTRICAL HYBRID RING NETWORK v Filed March 5, 1953 4 Sheets-Sheet 4 INPUT ADMITT VS. FREQUENCY OF WIDE ND YBRID RING WITH CAPACITANCE AT TERMINALS 2813 /binICORRECTED BY Zyyf ACCROSS INPUT TERMINAL.)

SHUNT CAPACITANCE OF 2.0M! AcRoss INPUT TERM.

'IO 20 3O 4O 5 6O 7O 8O 90 I00 II I20 I30 -9-IN 2.0,uyf ASSUMED B IN WITH son LOAD (b 0.428 AT e= NORMALIZED INPUT CONDUCTANCE BISUSCEPTANCE 2,735,986 liateetssl. Eeksee as nge.

creasing the band of, fregyencies over which a Magic T network is adapted to operate.

Ihetqtm, M gic, Ti, sgener o a i y of. electric l s saits. Some. f. wh ch r d s uss d inv Mic owav Duplexers by Smullin and Mgnftggmerygvol. 14; ofjhe M. I. T. Radiation Laboratory Series published by Mc- Graw-Hill. Most embodiments of MagidTliitworka??? limited in operation to a relatively narrow band of frequencies and are, therefore, termed frequency sensitive. However; one embodiment, a hybfid iin'g,6r riiig-difcizit, type of-Magic-Twhich 8 a of a closed loop of transmission line, may 'berriade to dp'erate over a comparativ'ely wide band of frequencies and is therefore called .ffrequency insensitive. The length of the line forming network because the one-wavelength loop is divided into 1 a. or. four arms, each approximately quarter wave ength, or

at all s s It' lias'been' found tliat the terminating"impedancs' at dutput trininaPpai'rs' sometimes comprisere'ac'tiv ponents'which haveaparticularly d" let'erious e6: operationof'a'widebandring';'

One object of the invention is to wide band hybrid 'rirignetwork.

Another object is to balance out the undesired reactive components of a wideban d ring.

Other objects will appearjfrom a study of the follow- 38 'LSPecification together h the drawings in which: Figure 1 is a schemat' iag ram of a 671/4 wide band hybrid ring; l

provide an imprpyed operable over a wide band'bf frequencies, the inyegting Figure 2 is an elaboration of Figure l for mathematical a y *.--'.s 1 r11 "1.

Figure 3 shows reactance and admittance curves of the ring of Figure l for purely resistive terminations;

Figure 4 gives the response curves of the ring of Figure1;and

Figure 5 cqrrespondsto Eigyre} and illustrates curves for terminations including reactive components.

One embodiment of the invention comprises a loop of two-conductor transmission line. The two ends of the line are connected t asse loopfbu'tf in making the connection, the twoc'oiiductors are twisted, or transposed. Four pairs of terminals arg spaiced at s ubs tantially equal distances arouridjt v W means the twist; or transposition, is located between we of the pairs of terminals. Alter; masses of terminals "srve as lnpufter rfiifialywhile tire remaining pairs of terminals are outpufter'minals'r As set forth hereinaboye, stray capacitance across the output terminals introduces an undesired reactive com- PQP l91lh qauivalen mpedance oti he 1:09p- Jae aaas tiye ,re aa e v i e"s ut1;u t rmina s s trans.- formed, ull... tran mi sion l ne. f rming the loop, int an equivalent inductive re ctance at the input terminals. Iiiorder to cancel out this equivalent inductive reactance, Rfig ipt ,isvcmmected' a ross. the input'ternipa s" It 1 assatqaas assay to re n the dde qce acitarice with the equivalent induct at certain portions of the operating frequency band, and one preferred condition is that the cl "c pa cg be approximately equal to the capacit anceat0ne oflhe pairs of output amina e Qthe mma a udes r hv vcapacitance will adetermi e h reina ter.

hyb id. r gs t w ll e ssa hat 9 prise"the"ring'ahdthat 13 in" f a ranspos on of the two conductors 13a and 13b. he jliiibt'ih'bf arms 11 and 14 is a P of inpu terminals lgansl ll. referred to simply as termin'a1"1 hereinafter. A seco nd pair of input terminals 18 and 1, referred to as terrfiinal; hereinafter; is located at" the'ljunction of arms 12 aridl3. Oii pair -of t'ilitfgltl t'tern'linals 21 and 22, 9?} 2. ip mes t he junc i oft m 11 L 1. vx le a. econd. pa r at ou pu ermi s zi called: germinal 3', i s lpcated,.at the junction ,qfiarms I. v -.r

in the first analysis of the operation of the ring in Figure 1, only the non-fact'ive'iinpedances (or conductances) 26, across terminals 21'and, 2'2,-"ane-z1;-acr5s terminals ;23,and,2.4, willbe considered. fConductaiices 26 and 27 may be the input conductances of resistive loads (not shown) connected to therespective terminal pairs. The optput conductance 28 of; thesignal source (not shown) supplying 'an electrical signal to the ring is connected across the terminals 16 and 17. Normally, .lpad conductance 2 6.is equal to conductance 21uriless impedance transformation is provided .inxtheringbhin the connections thereto.

- ,C onductnces 26 and gl, are relat ed to theconductance 28 of the source by a factor k, and the conductance of the xa smi iq :Lhefarmins ms 1. 4am .a'function offk' that, e: npu c nductance of the ring willimfiwh the source conductance 28 at the design center frequency o f the ring.

Because the equivalent circuit is balanced with respect to ground, only four of the possible eight nodal equations are neces r y to des ribe operatifi'n of the ring, and these are obtainedby'theapplication of Kirchholf's laws to the circuit of Figure 2, which is the equivalent of Figure l. The simultaneous equations are:

By solving Equations 1, 2, 3 and 4 for E4 there is obtained the desired result that:

This result is independent of frequency and load conditions at terminals 18 and 19. By substituting 5 in Equation 4 it is also apparent that for all frequencies E2=Es The condition of Equation 5 also simplifies Equations 1, 2, 3 and 4 so that the operation of the circuit may be described by two equations:

=E1Y112E2Y12 (la) 0=-E1Y12+E2Y22 From In: and 2a, the input and transfer admittance may be derived and power relationships obtained. Deriving first the normalized input admittance After substituting the equivalent for Yu, Y2: and Y12, Equation 7 becomes It should be noted here that the source conductance 28 is included in the input admittance equation, and, if the input admittance of the ring is desired, it may be obtained by subtracting 1 from Equation 8:

ym=ym--1 This is plotted in Figure 3.

The transfer admittance may be expressed by h Z22 X o o Y t/r- Yo E Yo and once again substituting the equivalent for Yn, Yes and Yrs, 10 becomes The power absorbed by the ring exclusive of that ab sorbed by the source con uctance 28 may be expressed Pm=ZL"1PRe(Ym) where and 1 P= I [1+ (210-1) cos 0P This power is maximum when which corresponds to the design center frequency of the ring and is equal to the maximum available power from the source or By normalizing 13 with respect to 13a an expression is obtained showing the power loss when the frequency is other than at design center Equation 14 defines a response curve for the wideband hybrid ring and in the subject application it is desirable that the bandwidth be maximum. Although an expression for bandwidth can be derived and diiferentiated with respect to k to find the optimum value of k, it is easier here to differentiate p with respect to k for any given angle of 0 and set the difierential equation equal to zero to obtain the optimum k. Thus 2 =0 [1+ 2 cos 0] Solving 15 for k A plot of the inverse of After substituting the value of Y(k=1) in the above Equation 17 becomes While the preceding analysis was carried out for purely resistive terminations, parallel capacitance across load conductances 26 and 27 is invariably encountered in practice. This capacitance, which may be stray and unavoidable or may be deliberately added, is indicated by a capacitor 29 in parallel with the load 26 and a capacitor 31 in parallel with the load 27. To accommodate the parallel resistancecapacitance loads at terminals 2 and 3, Yzz becomes where Y=JB=JwC and When Yzz is substituted in Equation 7 the normalized admittance for k=l becomes where tance can be made small over a wideband if equal capacitance equivalent to b=0.428 at b= 0.428 at 6:

are also placed across terminals 1 and 4. Condensers 32 and 33, respectively, supply the added capacitance.

The response of this capacity-loaded ring can then be evaluated from the normalized input admittance, which becomes Where gm is defined by Equation 20 and b=0.428 at a=g Then the response curve as plotted in Figure 4 is obtained from g.-,+1 =+o.-..1 b) 9in tan b- It will be noted in Fig. 5 that the addition of capacitor 32 (Fig. 1) tunes out the equivalent inductance 34 which arises from the impedance-transforming characteristics of the arms 11 and 14 acting on the capacitive reactance of condensers 29 and 31. The particular susceptance represented by capacitor 32 shifts the susceptance curve 36 up to the position of the dotted curve 37, which is tangent to the pure conductance line at 0:78. Between 0=55 and 0: the input admittance of the ring is composed almost entirely of conductance with practically no susceptance.

The angle 0 may be understood as a direct measure of frequency simply by equating a particular angle 0 to a particular frequency. For instance, if 0=78 for a frequency of 780 mc., the angle 0=55 corresponds to a frequency of 550 mc. and the angle 0: 85 corresponds to a frequency of 850 mc. Therefore, for a hybrid ring adjusted to these frequencies, the admittance would be composed of practically pure conductance between the frequencies of 550 mo. and 850 mc., and the usable bandwidth would be even greater than the indicated 300 mc., since the small susceptance at 0:50 and (i=, or even beyond, may have negligible effect on the operation. The usable bandwidth is not defined with exactness but is a matter of judgment, as is well-known to those skilled in the art.

Although this invention has been described in limited terms and related to specific embodiments, it will be obvious to those skilled in the art that modifications may be made therein within the scope of the invention as determined by the following claims.

What is claimed is:

1. A hybrid ring comprising first, second, third, and fourth pairs of two-wire transmission lines, said transmission lines being connected end to end to form a closed loop with the wires of one of said transmission lines being transposed to invert the polarity of signals passing therethrough; a first pair of input terminals at the junction of said first and fourth transmission lines; a second pair of input terminals at the junction of said second and third transmission lines; a source of electrical signals connected to said first pair of input terminals to energize said ring with a signal in a predetermined frequency band, each of said transmission lines being approximately a quarter wave long for frequencies in said band; a first pair of output terminals at the junction of said first and second transmission lines; a second pair of output terminals at the junction of said third and fourth transmission lines; a first load impedance connected between the terminals of said first pair of output terminals and comprising resistance and capacitance; a second load impedance connected be tween the terminals of said second pair of output terminals and comprising resistance and capacitance substantially equal respectively to the resistance and capacitance of said first impedance; and a capacitive reactance connected in parallel with said source between the terminals of said first pair of input terminals to cancel the effect of said capacitances in said load impedances thereby to make said hybrid ring operate over a broad band of frequencies.

2. The circuit of claim 1 in which the reactance of said capacitive reactance connected to said input terminals has substantially the same magnitude as a reactance of the capacitance of each of said impedances in said frequency band.

References Cited in the file of this patent UNITED STATES PATENTS 2,436,828 Ring Mar. 2, 1948 

